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Railways NTPC (Technical Ability) Engineering Mechanics and Strength of Materials Question Bank Engineering Mechanics

  • question_answer
                             Two hollow shafts of the same material have the same length and outside diameter. Shaft 1 has internal diameter equal to one-third of the outer diameter and shaft 2 has internal diameter equal to half of the outer diameter. If both the shafts are subject to the same torque, the ratio of their twists \[{{\theta }_{1}}/{{\theta }_{2}}\] will be equal  to:                                         

    A) 16/81               

    B) 8/27                                                                

    C) 19/27               

    D) 243/256          

    Correct Answer: D

    Solution :

    \[{{G}_{1}}={{G}_{2}},\] \[{{l}_{1}}={{l}_{2}},\] \[{{D}_{1}}={{D}_{2}},\] \[{{d}_{1}}=\frac{1}{3}{{D}_{1}}\] \[{{d}_{2}}=\frac{1}{2}{{D}_{2}},\] \[{{T}_{1}}={{T}_{2}}=T\] \[\frac{T}{J}=\frac{G,}{l}\] G, l and T being same for born the shafts, \[\theta =\,\,\propto \frac{1}{J}\] \[\frac{{{\theta }_{1}}}{{{\theta }_{2}}}=\frac{{{J}_{2}}}{{{J}_{1}}}=\frac{\frac{\pi }{32}D_{2}^{4}\,\left[ 1-{{\left( \frac{{{d}_{2}}}{{{D}_{2}}} \right)}^{4}} \right]}{\frac{\pi }{32}D_{1}^{4}\,\left[ 1-{{\left( \frac{{{d}_{1}}}{{{D}_{1}}} \right)}^{4}} \right]}\] \[\frac{\left[ 1-{{\left( \frac{1}{2} \right)}^{4}} \right]}{\left[ 1-{{\left( \frac{1}{3} \right)}^{4}} \right]}=\frac{\left( \frac{15}{16} \right)}{\left( \frac{80}{81} \right)}=\frac{243}{256}\]


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